Computes the posterior model probabilities for standard meta-analysis models
(null model vs. alternative model assuming either fixed- or random-effects, respectively).
These posterior probabilities are used to estimate the overall mean effect size
as the weighted average of the mean effect size estimates of the random- and
fixed-effect model as proposed by Gronau, Van Erp, Heck, Cesario, Jonas, &
Wagenmakers (2017, <doi:10.1080/23743603.2017.1326760>). The user can define
a wide range of non-informative or informative priors for the mean effect size
and the heterogeneity coefficient. Moreover, using pre-compiled Stan models,
meta-analysis with continuous and discrete moderators with Jeffreys-Zellner-Siow (JZS)
priors can be fitted and tested. This allows to compute Bayes factors and
perform Bayesian model averaging across random- and fixed-effects meta-analysis
with and without moderators. For a primer on Bayesian model-averaged meta-analysis,
see Gronau, Heck, Berkhout, Haaf, & Wagenmakers (2020, <doi:10.31234/osf.io/97qup>).